Thanks for the tips. After some browsing in FishBase I believe this fellow is Ocellate damselfish, also known as Princess damsel, latin name Pomacentrus vaiuli. The image in http://www.fishbase....30&what=species matches quite nicely.

I hope TMC publishing will continue soon their book series with one about damselfishes! The drawings in Lieske&Myers are quite not enough. Oh well, now that I browse through Allen & Steene there is a half-a-page photo of the princess in page 316!

Your fish definitely looks like the Princess Damsel on p. 316 of Allen & Steene, but the picture of an Ocellated Damsel in the new Humann book (p. 68) doesn't look like the same fish. Also, the Ocellated Damsel's range is shown to be Indonesia~Sumatra~Andaman Sea, which is much further west than Fiji.

So I think you're right about the Princess Damsel, but I'm not sure that the Princess Damsel and the Ocellated Damsel are the same, at least from the photos that I'm seeing.